In the field of microelectronics, particularly metrology, accurate measurement of linewidths on photomasks is a crucial first step in the production of devices having submicron feature size. In recent years, a useful, new technique for characterizing periodic topographic structures has been scatterometry. Scatterometry is a technique which involves directing a light beam, typically a laser, on an area to be characterized and measuring the angular distribution of the light which is elastically scattered from that area. It is nondestructive, noncontaminating and noninvasive. No sample preparation is necessary. Only a light beam impinges on the surface of interest, and nothing is changed in the sample during the measurement.
Prior art optical measurement systems form a different broad class of instrumentation used for linewidth measurements. Each of these prior art optical linewidth measurement systems provides an image profile of the feature to be measured and uses a particular edge detection algorithm to determine the linewidth. One of the most often encountered sources of error in submicron dimensional metrology is determining the location of the edge on the image profile of the feature. The modeling of formation of optical image profiles from thick submicron features is an area of active research according to C-M. Yuan, J. Shaw and W. Hopwell, "Modeling of optical alignment images for semiconductor structures," Proc. SPIE, Vol. 1088, pp. 392-402, 1989. The inverse problem, however, of prediction of linewidths from observed image profiles in a microscope, remains an open problem for thick submicron features as noted by D. Nyyssonen and B. Monteverde, "Linewidth Edge Detection Algorithm for Coherent Image Profiles," Proc. SPIE, vol. 1087, pp. 146-152, February 1989. This implies that there is no rigorous foundation for use of a particular edge detection methodology in an optical microscope as indicated by D. Nyyssonen, "Practical method for edge detection and focusing for linewidth measurements on wafers," Optical Engineering, pp. 81-85, January 1987. It is necessary to model the diffraction effects in order to understand the optical image produced by a particular feature. Analysis of diffraction from an arbitary object is complex. However, the problem is simplified if the diffracting feature is periodic (diffraction grating). In this case, the scattered field consists of distinct diffraction orders (.+-.n), whose angular position (.theta..sub.n) is given by the well known grating formula, ##EQU1## Here .theta..sub.i is the angle of incidence, .lambda. is the wavelength of the incident beam, and d is the period, or pitch, of the grating. The distribution of diffracted power among the various orders is related to the geometry of the diffraction grating. The inverse problem then consists of determining the parameters of interest (linewidth, height, sidewall angle) from a measurement of the diffracted power in the different orders. In this connection the use of coherent illumination and analysis of the diffraction pattern in the Fourier plane has been considered previously by H. P. Kleinknecht and H. Meier, "Linewidth Measurement on IC Masks and Wafers by Grating Test Patterns," Applied Optics, vol. 19, No. 4, pp. 525-533, Feb. 15, 1980. The use of an approximate analysis restricted the application of this technique to the case in which the angle of incidence was equal to Brewster's angle, and the period was greater than the wavelength. In addition, the previous treatment was best suited for a situation in which the linewidth to pitch ratio was approximately 0.25.